I see that proof, due to Euclid, as simpler because it doesn't require any facts about trigonometric functions.
It might be harder to write out in mathematical notation in one line, but maybe I should try (using set-builder notation or something).
It might be harder to write out in mathematical notation in one line, but maybe I should try (using set-builder notation or something).
> One plus the product of all primes is itself prime, and larger than all primes.
This omits a bunch of stuff, but it seems like less than the linked paper.
One plus the product of the first N primes is not necessarily prime. Consider 2 * 3 * 5 * 7 * 11 * 13 + 1 = 30031 = 59 * 509
Top prime's divisors'
product (plus one)'s factors are...?
Q.E.D., bitches!
The "top prime's divisors' product" would be equal to the top prime itself, so Randall's haiku asks "if there is a largest prime p, what are the divisors of (p+1)?" which doesn't create any contradiction (it could simply be divisible by various smaller primes!).
Maybe we should amend it to
Take factorial
of top prime, then add one: what
are the divisors? Factorial of
top prime, plus one: factor that!
Q.E.D., bitches!